0.5x=82/x

Solution for 0.5x=82/x equation:

0.5x=82/x

We move all terms to the left:

0.5x-(82/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

0.5x-(+82/x)=0

We get rid of parentheses

0.5x-82/x=0

We multiply all the terms by the denominator


(0.5x)*x-82=0

We add all the numbers together, and all the variables

(+0.5x)*x-82=0

We multiply parentheses

0x^2-82=0

We add all the numbers together, and all the variables

x^2-82=0

a = 1; b = 0; c = -82;
Δ = b2-4ac
Δ = 02-4·1·(-82)
Δ = 328
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{82}}{2*1}=\frac{0-2\sqrt{82}}{2}
=-\frac{2\sqrt{82}}{2}
=-\sqrt{82}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{82}}{2*1}=\frac{0+2\sqrt{82}}{2}
=\frac{2\sqrt{82}}{2}
=\sqrt{82}
$